Reproducing kernel banach spaces for machine learning

Authors:
Haizhang Zhang;Yuesheng Xu;Jun Zhang
Affiliations:
Department of Mathematics, Syracuse University, Syracuse, NY;Department of Mathematics, Syracuse University, Syracuse, NY;Department of Psychology, University of Michigan, Ann Arbor, MI
Venue:
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Year:
2009

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Abstract

Reproducing kernel Hilbert space (RKHS) methods have become powerful tools in machine learning. However, their kernels, which measure similarity of inputs, are required to be symmetric, constraining certain applications in practice. Furthermore, the celebrated representer theorem only applies to regularizers induced by the norm of an RKHS. To remove these limitations, we introduce the notion of reproducing kernel Banach spaces (RKBS) for pairs of reflexive Banach spaces of functions by making use of semi-inner-products and the duality mapping. As applications, we develop the framework of RKBS standard learning schemes including minimal norm interpolation, regularization network, and support vector machines. In particular, existence, uniqueness and representer theorems are established.